We generalize the nonaffine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the kernel polynomial method (KPM) for the computation of the vibrational density of states and the eigenmodes, including the $\mathrm{\Gamma }$ correlator of the affine force field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with $N={10}^4$ atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to ${10}^6$ atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with $N$.

• Received 4 April 2020
• Accepted 29 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.024108

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society